Solve 3rd Taylor Polynomial for (x-1)In(x) About x0=1 - Find Error Bound

[Newbatmath]

Hey guys! I am attempting to do this problem and have been working with it for awhile now. Once again, it is an issue of the textbook not being very clear and making me more confused than ever. Sadly, our teacher is still MIA.

Find the third Taylor polynomial P₃(x) for the function f(x)= (x-1)In(x) , about x₀ = 1; and use p₃(0.5) to approx. f(0.5). Find the upper bound for error /f(0.5) – p₃(0.5)/, then compare it to the actual error.

I know this is a tall order but any help you could give me that I could compare to my work here would be such a help! Thanks a bunch!

 

[whs]

What is the 'In(x)' in your function. Do you mean 'ln(x)'?

Otherwise this question is very straightforward. Just calculate the first 3rd Taylor polynomial and plug in numbers.

I don't see the problem?

 

[Newbatmath]

Yep, you are right. ln(x). Sorry about that. :) Thanks so much!

 

[Newbatmath]

Okay so I somehow got -4.25. Does anyone else think that is correct?

Anyone know how to find the actual error?